cat-and-mouse.xml

<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE nta PUBLIC '-//Uppaal Team//DTD Flat System 1.5//EN' 'http://www.it.uu.se/research/group/darts/uppaal/flat-1_5.dtd'>
<nta>
	<declaration>/** 
 * "Cat and Mouse" by Kim Guldstrand Larsen and Marius Mikučionis.
 * The model is about a cat chasing a mouse in a maze with a narrow passage.
 * Demonstrates the features of Stratego: 
 *   symbolic and SMC queries, TIGA synthesis and optimization using learning.
 * The system consists of four processes:
 * - Cat tracks the position and possible moves for the cat.
 * - Mouse tracks the position and possible moves for the mouse, 
 *   has an extra narrow passage to Cheese, that is not available to Cat.
 * - CatP models the cat player moves (up, left, down, right) with delay.
 * - MouseP models the mouse player moves (up, left, down, right) with delay.
 * The objective of the game is for Mouse to get to Cheese location and 
 * avoid being cought by Cat (detected when positions are equal).
 * Mouse is the player/controller with controllable movements.
 * Cat is the opponent/environment with uncontrollable movements.
 * The strategy synthesis and optimization queries achieve the specified 
 * objectives by restricting controlable actions.
 */
const int CP = 2; // delay step size for Cat
const int MP = 1; // delay step size for Mouse
broadcast chan cu, cl, cd, cr; // cat: up, left, down, right
broadcast chan mu, ml, md, mr; // mouse: up, left, down, right</declaration>
	<template>
		<name x="5" y="5">Cat</name>
		<declaration>int s = 0;</declaration>
		<location id="id0" x="34" y="-170">
			<name x="24" y="-204">L1</name>
		</location>
		<location id="id1" x="-102" y="-170">
			<name x="-112" y="-204">L0</name>
		</location>
		<location id="id2" x="-102" y="-34">
			<name x="-136" y="-42">L4</name>
		</location>
		<location id="id3" x="170" y="-170">
			<name x="160" y="-204">L2</name>
		</location>
		<location id="id4" x="306" y="-170">
			<name x="297" y="-204">Cheese</name>
		</location>
		<location id="id5" x="306" y="-34">
			<name x="297" y="-17">L6</name>
		</location>
		<location id="id6" x="170" y="-34">
			<name x="161" y="-17">L5</name>
		</location>
		<location id="id7" x="170" y="102">
			<name x="160" y="68">L9</name>
		</location>
		<location id="id8" x="34" y="102">
			<name x="24" y="68">L8</name>
		</location>
		<location id="id9" x="-102" y="102">
			<name x="-136" y="93">L7</name>
		</location>
		<location id="id10" x="-102" y="238">
			<name x="-144" y="229">L10</name>
		</location>
		<location id="id11" x="34" y="238">
			<name x="25" y="255">L11</name>
		</location>
		<location id="id12" x="170" y="238">
			<name x="153" y="255">L12</name>
		</location>
		<location id="id13" x="306" y="238">
			<name x="297" y="255">L13</name>
		</location>
		<init ref="id1"/>
		<transition id="id14" controllable="false">
			<source ref="id6"/>
			<target ref="id3"/>
			<label kind="synchronisation" x="187" y="-119">cu?</label>
			<label kind="assignment" x="187" y="-102">s=2</label>
			<nail x="187" y="-68"/>
			<nail x="187" y="-136"/>
		</transition>
		<transition id="id15" controllable="false">
			<source ref="id5"/>
			<target ref="id6"/>
			<label kind="synchronisation" x="205" y="-34">cl?</label>
			<label kind="assignment" x="238" y="-34">s=5</label>
			<nail x="280" y="-17"/>
			<nail x="195" y="-17"/>
		</transition>
		<transition id="id16" controllable="false">
			<source ref="id12"/>
			<target ref="id13"/>
			<label kind="synchronisation" x="204" y="238">cr?</label>
			<label kind="assignment" x="238" y="238">s=13</label>
			<nail x="204" y="255"/>
			<nail x="272" y="255"/>
		</transition>
		<transition id="id17" controllable="false">
			<source ref="id3"/>
			<target ref="id0"/>
			<label kind="synchronisation" x="68" y="-170">cl?</label>
			<label kind="assignment" x="102" y="-170">s=1</label>
			<nail x="136" y="-153"/>
			<nail x="68" y="-153"/>
		</transition>
		<transition id="id18" controllable="false">
			<source ref="id0"/>
			<target ref="id1"/>
			<label kind="synchronisation" x="-68" y="-170">cl?</label>
			<label kind="assignment" x="-34" y="-170">s=0</label>
			<nail x="0" y="-153"/>
			<nail x="-68" y="-153"/>
		</transition>
		<transition id="id19" controllable="false">
			<source ref="id1"/>
			<target ref="id2"/>
			<label kind="synchronisation" x="-85" y="-119">cd?</label>
			<label kind="assignment" x="-85" y="-102">s=4</label>
			<nail x="-85" y="-136"/>
			<nail x="-85" y="-68"/>
		</transition>
		<transition id="id20" controllable="false">
			<source ref="id2"/>
			<target ref="id9"/>
			<label kind="synchronisation" x="-85" y="17">cd?</label>
			<label kind="assignment" x="-85" y="34">s=7</label>
			<nail x="-85" y="0"/>
			<nail x="-85" y="68"/>
		</transition>
		<transition id="id21" controllable="false">
			<source ref="id9"/>
			<target ref="id10"/>
			<label kind="synchronisation" x="-85" y="153">cd?</label>
			<label kind="assignment" x="-85" y="170">s=10</label>
			<nail x="-85" y="136"/>
			<nail x="-85" y="204"/>
		</transition>
		<transition id="id22" controllable="false">
			<source ref="id10"/>
			<target ref="id11"/>
			<label kind="synchronisation" x="-68" y="221">cr?</label>
			<label kind="assignment" x="-34" y="221">s=11</label>
		</transition>
		<transition id="id23" controllable="false">
			<source ref="id8"/>
			<target ref="id11"/>
			<label kind="synchronisation" x="51" y="153">cd?</label>
			<label kind="assignment" x="51" y="170">s=11</label>
			<nail x="51" y="136"/>
			<nail x="51" y="204"/>
		</transition>
		<transition id="id24" controllable="false">
			<source ref="id8"/>
			<target ref="id9"/>
			<label kind="synchronisation" x="-68" y="102">cl?</label>
			<label kind="assignment" x="-34" y="102">s=7</label>
			<nail x="0" y="119"/>
			<nail x="-76" y="119"/>
		</transition>
		<transition id="id25" controllable="false">
			<source ref="id0"/>
			<target ref="id3"/>
			<label kind="synchronisation" x="68" y="-187">cr?</label>
			<label kind="assignment" x="102" y="-187">s=2</label>
		</transition>
		<transition id="id26" controllable="false">
			<source ref="id1"/>
			<target ref="id0"/>
			<label kind="synchronisation" x="-68" y="-187">cr?</label>
			<label kind="assignment" x="-34" y="-187">s=1</label>
		</transition>
		<transition id="id27" controllable="false">
			<source ref="id2"/>
			<target ref="id1"/>
			<label kind="synchronisation" x="-136" y="-119">cu?</label>
			<label kind="assignment" x="-136" y="-102">s=0</label>
		</transition>
		<transition id="id28" controllable="false">
			<source ref="id9"/>
			<target ref="id2"/>
			<label kind="synchronisation" x="-136" y="17">cu?</label>
			<label kind="assignment" x="-136" y="34">s=4</label>
		</transition>
		<transition id="id29" controllable="false">
			<source ref="id11"/>
			<target ref="id8"/>
			<label kind="synchronisation" x="0" y="153">cu?</label>
			<label kind="assignment" x="0" y="170">s=8</label>
		</transition>
		<transition id="id30" controllable="false">
			<source ref="id12"/>
			<target ref="id7"/>
			<label kind="synchronisation" x="170" y="153">cu?</label>
			<label kind="assignment" x="170" y="170">s=9</label>
		</transition>
		<transition id="id31" controllable="false">
			<source ref="id3"/>
			<target ref="id6"/>
			<label kind="synchronisation" x="144" y="-119">cd?</label>
			<label kind="assignment" x="144" y="-102">s=5</label>
		</transition>
		<transition id="id32" controllable="false">
			<source ref="id4"/>
			<target ref="id3"/>
			<label kind="synchronisation" x="204" y="-187">cl?</label>
			<label kind="assignment" x="238" y="-187">s=2</label>
		</transition>
		<transition id="id33" controllable="false">
			<source ref="id5"/>
			<target ref="id4"/>
			<label kind="synchronisation" x="306" y="-119">cu?</label>
			<label kind="assignment" x="306" y="-102">s=3</label>
		</transition>
		<transition id="id34" controllable="false">
			<source ref="id6"/>
			<target ref="id5"/>
			<label kind="synchronisation" x="204" y="-51">cr?</label>
			<label kind="assignment" x="238" y="-51">s=6</label>
		</transition>
		<transition id="id35" controllable="false">
			<source ref="id7"/>
			<target ref="id8"/>
			<label kind="synchronisation" x="68" y="85">cl?</label>
			<label kind="assignment" x="102" y="85">s=8</label>
		</transition>
		<transition id="id36" controllable="false">
			<source ref="id9"/>
			<target ref="id8"/>
			<label kind="synchronisation" x="-68" y="85">cr?</label>
			<label kind="assignment" x="-34" y="85">s=8</label>
		</transition>
		<transition id="id37" controllable="false">
			<source ref="id10"/>
			<target ref="id9"/>
			<label kind="synchronisation" x="-136" y="153">cu?</label>
			<label kind="assignment" x="-136" y="170">s=7</label>
		</transition>
		<transition id="id38" controllable="false">
			<source ref="id11"/>
			<target ref="id10"/>
			<label kind="synchronisation" x="-68" y="238">cl?</label>
			<label kind="assignment" x="-34" y="238">s=10</label>
			<nail x="8" y="255"/>
			<nail x="-76" y="255"/>
		</transition>
		<transition id="id39" controllable="false">
			<source ref="id11"/>
			<target ref="id12"/>
			<label kind="synchronisation" x="68" y="221">cr?</label>
			<label kind="assignment" x="102" y="221">s=12</label>
		</transition>
		<transition id="id40" controllable="false">
			<source ref="id13"/>
			<target ref="id12"/>
			<label kind="synchronisation" x="204" y="221">cl?</label>
			<label kind="assignment" x="238" y="221">s=12</label>
		</transition>
	</template>
	<template>
		<name x="5" y="5">Mouse</name>
		<declaration>int s = 13;</declaration>
		<location id="id41" x="34" y="-170">
			<name x="24" y="-204">L1</name>
		</location>
		<location id="id42" x="-102" y="-170">
			<name x="-112" y="-204">L0</name>
		</location>
		<location id="id43" x="-102" y="-34">
			<name x="-136" y="-42">L4</name>
		</location>
		<location id="id44" x="170" y="-170">
			<name x="160" y="-204">L2</name>
		</location>
		<location id="id45" x="306" y="-170">
			<name x="280" y="-204">Cheese</name>
		</location>
		<location id="id46" x="306" y="-34">
			<name x="297" y="-17">L6</name>
		</location>
		<location id="id47" x="170" y="-34">
			<name x="136" y="-42">L5</name>
		</location>
		<location id="id48" x="170" y="102">
			<name x="187" y="93">L9</name>
		</location>
		<location id="id49" x="34" y="102">
			<name x="24" y="68">L8</name>
		</location>
		<location id="id50" x="-102" y="102">
			<name x="-136" y="93">L7</name>
		</location>
		<location id="id51" x="-102" y="238">
			<name x="-144" y="229">L10</name>
		</location>
		<location id="id52" x="34" y="238">
			<name x="25" y="255">L11</name>
		</location>
		<location id="id53" x="170" y="238">
			<name x="153" y="255">L12</name>
		</location>
		<location id="id54" x="306" y="238">
			<name x="296" y="204">L13</name>
		</location>
		<init ref="id54"/>
		<transition id="id55">
			<source ref="id47"/>
			<target ref="id44"/>
			<label kind="synchronisation" x="187" y="-118">mu?</label>
			<label kind="assignment" x="187" y="-101">s=2</label>
			<nail x="187" y="-59"/>
			<nail x="187" y="-144"/>
		</transition>
		<transition id="id56">
			<source ref="id46"/>
			<target ref="id47"/>
			<label kind="synchronisation" x="204" y="-34">ml?</label>
			<label kind="assignment" x="238" y="-34">s=5</label>
			<nail x="280" y="-17"/>
			<nail x="195" y="-17"/>
		</transition>
		<transition id="id57">
			<source ref="id53"/>
			<target ref="id54"/>
			<label kind="synchronisation" x="204" y="238">mr?</label>
			<label kind="assignment" x="238" y="238">s=13</label>
			<nail x="204" y="255"/>
			<nail x="272" y="255"/>
		</transition>
		<transition id="id58">
			<source ref="id44"/>
			<target ref="id41"/>
			<label kind="synchronisation" x="68" y="-170">ml?</label>
			<label kind="assignment" x="102" y="-170">s=1</label>
			<nail x="136" y="-153"/>
			<nail x="68" y="-153"/>
		</transition>
		<transition id="id59">
			<source ref="id41"/>
			<target ref="id42"/>
			<label kind="synchronisation" x="-68" y="-170">ml?</label>
			<label kind="assignment" x="-34" y="-170">s=0</label>
			<nail x="0" y="-153"/>
			<nail x="-68" y="-153"/>
		</transition>
		<transition id="id60">
			<source ref="id42"/>
			<target ref="id43"/>
			<label kind="synchronisation" x="-85" y="-119">md?</label>
			<label kind="assignment" x="-85" y="-102">s=4</label>
			<nail x="-85" y="-136"/>
			<nail x="-85" y="-68"/>
		</transition>
		<transition id="id61">
			<source ref="id43"/>
			<target ref="id50"/>
			<label kind="synchronisation" x="-85" y="17">md?</label>
			<label kind="assignment" x="-85" y="34">s=7</label>
			<nail x="-85" y="0"/>
			<nail x="-85" y="68"/>
		</transition>
		<transition id="id62">
			<source ref="id50"/>
			<target ref="id51"/>
			<label kind="synchronisation" x="-85" y="153">md?</label>
			<label kind="assignment" x="-85" y="170">s=10</label>
			<nail x="-85" y="136"/>
			<nail x="-85" y="204"/>
		</transition>
		<transition id="id63">
			<source ref="id51"/>
			<target ref="id52"/>
			<label kind="synchronisation" x="-68" y="221">mr?</label>
			<label kind="assignment" x="-34" y="221">s=11</label>
		</transition>
		<transition id="id64">
			<source ref="id49"/>
			<target ref="id52"/>
			<label kind="synchronisation" x="51" y="153">md?</label>
			<label kind="assignment" x="51" y="170">s=11</label>
			<nail x="51" y="136"/>
			<nail x="51" y="204"/>
		</transition>
		<transition id="id65">
			<source ref="id47"/>
			<target ref="id48"/>
			<label kind="synchronisation" x="136" y="17">md?</label>
			<label kind="assignment" x="136" y="34">s=9</label>
			<label kind="comments" x="221" y="25">Narrow passage
only mice can use.</label>
		</transition>
		<transition id="id66">
			<source ref="id48"/>
			<target ref="id47"/>
			<label kind="synchronisation" x="187" y="17">mu?</label>
			<label kind="assignment" x="187" y="34">s=5</label>
			<nail x="187" y="76"/>
			<nail x="187" y="0"/>
		</transition>
		<transition id="id67">
			<source ref="id49"/>
			<target ref="id50"/>
			<label kind="synchronisation" x="-68" y="102">ml?</label>
			<label kind="assignment" x="-34" y="102">s=7</label>
			<nail x="0" y="119"/>
			<nail x="-76" y="119"/>
		</transition>
		<transition id="id68">
			<source ref="id41"/>
			<target ref="id44"/>
			<label kind="synchronisation" x="68" y="-187">mr?</label>
			<label kind="assignment" x="102" y="-187">s=2</label>
		</transition>
		<transition id="id69">
			<source ref="id42"/>
			<target ref="id41"/>
			<label kind="synchronisation" x="-68" y="-187">mr?</label>
			<label kind="assignment" x="-34" y="-187">s=1</label>
		</transition>
		<transition id="id70">
			<source ref="id43"/>
			<target ref="id42"/>
			<label kind="synchronisation" x="-136" y="-119">mu?</label>
			<label kind="assignment" x="-136" y="-102">s=0</label>
		</transition>
		<transition id="id71">
			<source ref="id50"/>
			<target ref="id43"/>
			<label kind="synchronisation" x="-136" y="17">mu?</label>
			<label kind="assignment" x="-136" y="34">s=4</label>
		</transition>
		<transition id="id72">
			<source ref="id52"/>
			<target ref="id49"/>
			<label kind="synchronisation" x="0" y="153">mu?</label>
			<label kind="assignment" x="0" y="170">s=8</label>
		</transition>
		<transition id="id73">
			<source ref="id53"/>
			<target ref="id48"/>
			<label kind="synchronisation" x="170" y="153">mu?</label>
			<label kind="assignment" x="170" y="170">s=9</label>
		</transition>
		<transition id="id74">
			<source ref="id44"/>
			<target ref="id47"/>
			<label kind="synchronisation" x="144" y="-119">md?</label>
			<label kind="assignment" x="144" y="-102">s=5</label>
		</transition>
		<transition id="id75">
			<source ref="id45"/>
			<target ref="id44"/>
			<label kind="synchronisation" x="204" y="-187">ml?</label>
			<label kind="assignment" x="238" y="-187">s=2</label>
		</transition>
		<transition id="id76">
			<source ref="id46"/>
			<target ref="id45"/>
			<label kind="synchronisation" x="306" y="-119">mu?</label>
			<label kind="assignment" x="306" y="-102">s=3</label>
		</transition>
		<transition id="id77">
			<source ref="id47"/>
			<target ref="id46"/>
			<label kind="synchronisation" x="204" y="-51">mr?</label>
			<label kind="assignment" x="238" y="-51">s=6</label>
		</transition>
		<transition id="id78">
			<source ref="id48"/>
			<target ref="id49"/>
			<label kind="synchronisation" x="68" y="85">ml?</label>
			<label kind="assignment" x="102" y="85">s=8</label>
		</transition>
		<transition id="id79">
			<source ref="id50"/>
			<target ref="id49"/>
			<label kind="synchronisation" x="-68" y="85">mr?</label>
			<label kind="assignment" x="-34" y="85">s=8</label>
		</transition>
		<transition id="id80">
			<source ref="id51"/>
			<target ref="id50"/>
			<label kind="synchronisation" x="-136" y="153">mu?</label>
			<label kind="assignment" x="-136" y="170">s=7</label>
		</transition>
		<transition id="id81">
			<source ref="id52"/>
			<target ref="id51"/>
			<label kind="synchronisation" x="-68" y="238">ml?</label>
			<label kind="assignment" x="-34" y="238">s=10</label>
			<nail x="8" y="255"/>
			<nail x="-76" y="255"/>
		</transition>
		<transition id="id82">
			<source ref="id52"/>
			<target ref="id53"/>
			<label kind="synchronisation" x="68" y="221">mr?</label>
			<label kind="assignment" x="102" y="221">s=12</label>
		</transition>
		<transition id="id83">
			<source ref="id54"/>
			<target ref="id53"/>
			<label kind="synchronisation" x="204" y="221">ml?</label>
			<label kind="assignment" x="238" y="221">s=12</label>
		</transition>
	</template>
	<template>
		<name>CatP</name>
		<declaration>clock x;</declaration>
		<location id="id84" x="204" y="-34">
			<name x="195" y="-25">Move</name>
			<urgent/>
		</location>
		<location id="id85" x="102" y="-34">
			<name x="51" y="-51">Idle</name>
			<label kind="invariant" x="51" y="-34">x&lt;=CP</label>
		</location>
		<init ref="id85"/>
		<transition id="id86" controllable="false">
			<source ref="id85"/>
			<target ref="id84"/>
			<label kind="guard" x="127" y="-110">x&gt;=CP</label>
			<label kind="assignment" x="127" y="-93">x=0</label>
			<nail x="102" y="-93"/>
			<nail x="204" y="-93"/>
		</transition>
		<transition id="id87" controllable="false">
			<source ref="id84"/>
			<target ref="id85"/>
			<label kind="synchronisation" x="144" y="-76">cu!</label>
			<nail x="178" y="-59"/>
			<nail x="136" y="-59"/>
		</transition>
		<transition id="id88" controllable="false">
			<source ref="id84"/>
			<target ref="id85"/>
			<label kind="synchronisation" x="144" y="-59">cr!</label>
			<nail x="178" y="-42"/>
			<nail x="136" y="-42"/>
		</transition>
		<transition id="id89" controllable="false">
			<source ref="id84"/>
			<target ref="id85"/>
			<label kind="synchronisation" x="144" y="-42">cd!</label>
			<nail x="178" y="-25"/>
			<nail x="136" y="-25"/>
		</transition>
		<transition id="id90" controllable="false">
			<source ref="id84"/>
			<target ref="id85"/>
			<label kind="synchronisation" x="143" y="-25">cl!</label>
			<nail x="178" y="-8"/>
			<nail x="136" y="-8"/>
		</transition>
	</template>
	<template>
		<name>MouseP</name>
		<declaration>clock x;</declaration>
		<location id="id91" x="204" y="-34">
			<name x="195" y="-25">Move</name>
			<urgent/>
		</location>
		<location id="id92" x="102" y="-34">
			<name x="51" y="-51">Idle</name>
			<label kind="invariant" x="51" y="-34">x&lt;=MP</label>
		</location>
		<init ref="id92"/>
		<transition id="id93" controllable="false">
			<source ref="id92"/>
			<target ref="id91"/>
			<label kind="guard" x="127" y="-110">x&gt;=MP</label>
			<label kind="assignment" x="127" y="-93">x=0</label>
			<label kind="comments" x="51" y="-153">Delay transition
must be uncontrollable.</label>
			<nail x="102" y="-93"/>
			<nail x="204" y="-93"/>
		</transition>
		<transition id="id94">
			<source ref="id91"/>
			<target ref="id92"/>
			<label kind="synchronisation" x="144" y="-76">mu!</label>
			<nail x="178" y="-59"/>
			<nail x="136" y="-59"/>
		</transition>
		<transition id="id95">
			<source ref="id91"/>
			<target ref="id92"/>
			<label kind="synchronisation" x="144" y="-59">mr!</label>
			<nail x="178" y="-42"/>
			<nail x="136" y="-42"/>
		</transition>
		<transition id="id96">
			<source ref="id91"/>
			<target ref="id92"/>
			<label kind="synchronisation" x="144" y="-42">md!</label>
			<nail x="178" y="-25"/>
			<nail x="136" y="-25"/>
		</transition>
		<transition id="id97">
			<source ref="id91"/>
			<target ref="id92"/>
			<label kind="synchronisation" x="143" y="-25">ml!</label>
			<nail x="178" y="-8"/>
			<nail x="136" y="-8"/>
		</transition>
	</template>
	<system>clock time; // used in minimization queries

system Cat, Mouse, CatP, MouseP;
</system>
	<queries>
		<query>
			<formula/>
			<comment>// GOAL: can Mouse reach Cheese?</comment>
		</query>
		<query>
			<formula>E&lt;&gt; Mouse.Cheese                                // Can Mouse reach Cheese?</formula>
			<comment>Expect YES, satisfied, Mouse can reach Cheese.
The query also loads a witness trace into Symbolic Simulator.</comment>
			<option key="--diagnostic" value="0"/>
		</query>
		<query>
			<formula>simulate [&lt;=100; 20] { Mouse.s }                // Where is Mouse most of the time?</formula>
			<comment>Expect trajectory all over entire maze, locations 0 through 12.
Inspect the simulations by right-clicking the query.</comment>
		</query>
		<query>
			<formula>simulate [&lt;=100; 100] { Mouse.s } : 1 : Mouse.Cheese   // Show trajectory of Mouse raching Cheese</formula>
			<comment>Expect a trajectory through random locations eventually reaching value 3 (Cheese location).</comment>
			<option key="--diagnostic" value="0"/>
		</query>
		<query>
			<formula>Pr[&lt;=1000](&lt;&gt; Mouse.Cheese)                     // Probability of Mouse reaching Cheese?</formula>
			<comment>Expect close to 100%, i.e. given enough time Mouse will eventually reach Cheese.
Cumulative Probability Distribution (right-click on the query) shows that it takes about 147 time units on average.
The query also provides a trace for Concrete Simulator to step through.</comment>
			<option key="--alpha" value="0.005"/>
			<option key="--epsilon" value="0.005"/>
		</query>
		<query>
			<formula/>
			<comment/>
		</query>
		<query>
			<formula/>
			<comment>// OPTIMIZE: strategy for Mouse to reach Cheese as Fast as possible</comment>
		</query>
		<query>
			<formula>strategy Fast = minE(time) [&lt;=100] { Mouse.location } -&gt; {} : &lt;&gt; Mouse.Cheese  // Minimize expected time for Mouse reaching Cheese</formula>
			<comment>Expect success.
The resulting strategy can be used in SMC and learning queries.</comment>
		</query>
		<query>
			<formula>simulate [&lt;=100; 20] { Mouse.s } under Fast     // Where is Mouse while using Fast strategy?</formula>
			<comment>Expect homing to and motion between locations 2, 3, 5, 6 around Cheese at 3.</comment>
		</query>
		<query>
			<formula>Pr[&lt;=100](&lt;&gt; Mouse.Cheese) under Fast &gt;= Pr[&lt;=100](&lt;&gt; Mouse.Cheese)  // Compare probabilities of Mouse reaching Cheese with and without Fast</formula>
			<comment>Expect YES, satisfied.
The comparison plot shows 0.5 before the first 5 time units (could not distinguish as Mouse is never at Cheese in both cases)
and then 1 (probability with Fast is strictly greater than without).</comment>
		</query>
		<query>
			<formula>Pr[&lt;=100](&lt;&gt; Mouse.Cheese) under Fast           // Probability of Mouse reaching Cheese under Fast</formula>
			<comment>Expect 100%.
Cumulative Probability Distribution shows that Mouse reaches Cheese always in exactly 5 time units.</comment>
			<option key="--alpha" value="0.005"/>
			<option key="--epsilon" value="0.005"/>
		</query>
		<query>
			<formula/>
			<comment/>
		</query>
		<query>
			<formula/>
			<comment>// Evaluate SAFETY</comment>
		</query>
		<query>
			<formula>E&lt;&gt; Cat.Cheese                                  // Can Cat get to Cheese?</formula>
			<comment>Expect YES, satisfied, Cat can get to Cheese too.
A witness trace is loaded into Symbolic Simulator.</comment>
			<option key="--diagnostic" value="0"/>
		</query>
		<query>
			<formula>E&lt;&gt; Cat.s == Mouse.s                            // Can Cat catch Mouse?</formula>
			<comment>Expect YES, satisfied.
A witness trace is loaded into Symbolic Simulator.</comment>
			<option key="--diagnostic" value="0"/>
		</query>
		<query>
			<formula>simulate [&lt;=100; 20] { Cat.s }                  // Where is Cat most of the time?</formula>
			<comment>Expect the location to vary all over the maze, values 0 through 12.</comment>
		</query>
		<query>
			<formula>simulate [&lt;=100] { 13*(Cat.s==Mouse.s), Cat.s, Mouse.s }   // Cat and Mouse trajectories with their collisions</formula>
			<comment>Expect trajectories of Cat and Mouse and sometimes collision marked in red reaching value 13.</comment>
		</query>
		<query>
			<formula>simulate [&lt;=100; 100] { 13*(Cat.s==Mouse.s), Cat.s, Mouse.s } : 1 : Cat.s==Mouse.s     // Find 1 trajectory where Mouse is cought</formula>
			<comment>Expect one trajectory where Cat and Mouse locations collide definately</comment>
			<option key="--diagnostic" value="0"/>
		</query>
		<query>
			<formula>Pr[&lt;=1000](&lt;&gt; Cat.s == Mouse.s)                 // Probability of Cat catching Mouse?</formula>
			<comment>Expect probability close to 100%
Cumulative Probability Distribution (right-click on the query) shows Mouse is cought in 44.3 time units on average.
A concrete trace leading to collision is loaded into Concrete Simulator.</comment>
			<option key="--alpha" value="0.005"/>
			<option key="--epsilon" value="0.005"/>
			<option key="--diagnostic" value="0"/>
		</query>
		<query>
			<formula/>
			<comment/>
		</query>
		<query>
			<formula/>
			<comment>// Evaluate SAFETY of Fast strategy</comment>
		</query>
		<query>
			<formula>simulate [&lt;=100; 20] { Cat.s } under Fast       // Where is Cat when Mouse uses Fast strategy?</formula>
			<comment>Expect trajectories all over the maze, similarly to when Mouse is not using Fast strategy.</comment>
		</query>
		<query>
			<formula>simulate [&lt;=100] { 13*(Cat.s==Mouse.s), Cat.s, Mouse.s } under Fast // Show trajectories of Cat and Mouse and their collisions</formula>
			<comment>Expect to see trajectories of Cat and Mouse locations and sometimes red getting to 13 when they collide.</comment>
		</query>
		<query>
			<formula>simulate [&lt;=100; 100] { 13*(Cat.s==Mouse.s), Cat.s, Mouse.s } : 1 : Cat.s==Mouse.s under Fast     // Find how Mouse is cought under Fast</formula>
			<comment>Expect Mouse to home-in to and stay around Cheese, while Cat moves randomly and eventually arrives to location equal to Mouse's.</comment>
		</query>
		<query>
			<formula>Pr[&lt;=1000](&lt;&gt; Cat.s == Mouse.s) under Fast &gt;= Pr[&lt;=1000](&lt;&gt; Cat.s == Mouse.s)  // Is Fast strategy safer than no strategy?</formula>
			<comment>Expect success.
The comparison plot shows 1 in the beginning -- Fast strategy is safer than no strategy in the very beginning, 
but later 0 -- less safe later,
and eventually 0.5 -- the probabilities could not be distinguished.</comment>
		</query>
		<query>
			<formula>Pr[&lt;=1000](&lt;&gt; Cat.s == Mouse.s) under Fast      // Probability of Cat catching Mouse using Fast strategy?</formula>
			<comment>Expect close to 100%.
Cumulative Proability Distribution plot shows that it takes 135.8 time units on average
(takes longer than when Mouse is not rushing to Cheese)</comment>
			<option key="--alpha" value="0.005"/>
			<option key="--epsilon" value="0.005"/>
		</query>
		<query>
			<formula/>
			<comment/>
		</query>
		<query>
			<formula/>
			<comment>// SAFETY strategy for Mouse to avoid Cat</comment>
		</query>
		<query>
			<formula>strategy Safe = control: A[] Cat.s != Mouse.s   // Can Mouse avoid Cat?</formula>
			<comment>Expect success.
The resulting strategy can be used in symbolic (E&lt;&gt;, A[] etc), SMC and learning queries.</comment>
		</query>
		<query>
			<formula>simulate [&lt;=100; 20] { Cat.s } under Safe       // Where is Cat most of the time under Safe?</formula>
			<comment>Expect trajectory all over the maze</comment>
		</query>
		<query>
			<formula>simulate [&lt;=100; 20] { Mouse.s } under Safe     // Where is Mouse most of the time under Safe?</formula>
			<comment>Expect trajectory all over the maze</comment>
		</query>
		<query>
			<formula>simulate [&lt;=100; 104] { 14*(Cat.s==Mouse.s), Cat.s, Mouse.s } : 1 : Cat.s==Mouse.s under Safe     // Find trajectory of Cat catching Mouse using Safe strategy</formula>
			<comment>Expect failure: such trajectory cannot be found.
Also the probability is estimated below 5% with 99% confidence level.</comment>
			<option key="--alpha" value="0.01"/>
		</query>
		<query>
			<formula>Pr[&lt;=100](&lt;&gt; Cat.s == Mouse.s) under Safe       // Probability of Cat catching Mouse using Safe?</formula>
			<comment>Expect probability to be below 0.5% with 99% confidence.</comment>
			<option key="--alpha" value="0.01"/>
			<option key="--epsilon" value="0.005"/>
		</query>
		<query>
			<formula>A[] Cat.s != Mouse.s under Safe                 // Can Mouse avoid Cat by using Safe strategy?</formula>
			<comment>Expect YES, satisfied, i.e. there is absolutely no way for Cat to catch Mouse using Safe strategy.</comment>
		</query>
		<query>
			<formula/>
			<comment/>
		</query>
		<query>
			<formula/>
			<comment>// Evaluate PERFORMANCE of the Safe strategy</comment>
		</query>
		<query>
			<formula>Pr[&lt;=1000](&lt;&gt; Mouse.Cheese) under Safe &gt;= Pr[&lt;=1000](&lt;&gt; Mouse.Cheese)  // Is Mouse better at reaching Cheese with or without Safe strategy?</formula>
			<comment>Expect YES, the probability of Mouse reaching Cheese is greater with Safe strategy.
The Comparison plot shows 1 up to time 650 -- Safe strategy is better than no strategy, 
but later it shows 0.5 -- it could not distinguish the probabilities from that point.</comment>
		</query>
		<query>
			<formula>Pr[&lt;=1000](&lt;&gt; Mouse.Cheese) under Fast &gt;= Pr[&lt;=1000](&lt;&gt; Mouse.Cheese) under Safe // Is Mouse better at reaching Cheese with Fast or Safe strategy?</formula>
			<comment>Expect YES, the probability of Mouse reaching Cheese greater with Fast than Safe strategy.
The Comparison plot shows 1 up to time 470 -- Fast strategy is better than Safe strategy, 
and later it shows 0.5 -- it could not distinguish the probabilities from that point.</comment>
		</query>
		<query>
			<formula>Pr[&lt;=1000](&lt;&gt; Mouse.Cheese) under Safe          // Probability of Mouse reaching Cheese using Safe</formula>
			<comment>Expect probability close to 100%.
Cumulative Probability Distribution shows that Mouse reaches Cheese within 124 time units on average
-- better than without strategy, but nowhere near the result of using Fast strategy (5 time units).</comment>
			<option key="--alpha" value="0.005"/>
			<option key="--epsilon" value="0.005"/>
		</query>
		<query>
			<formula/>
			<comment/>
		</query>
		<query>
			<formula/>
			<comment>// SAFE &amp; OPTIMAL: get to Cheese quick without getting cought</comment>
		</query>
		<query>
			<formula>strategy SafeFast = minE(time) [&lt;=100] { Cat.location, Mouse.location } -&gt; {} : &lt;&gt; Mouse.Cheese under Safe // Optimize Safe strategy for Mouse to reach Cheese in minimal time.</formula>
			<comment>Expect success.
The resulting strategy can be used only in SMC queries.</comment>
		</query>
		<query>
			<formula>simulate [&lt;=100; 20] { Cat.s } under SafeFast      // Where is Cat under SafeFast?</formula>
			<comment>Expect the location trajectory to be all over the maze from 0 through 12.</comment>
		</query>
		<query>
			<formula>simulate [&lt;=100; 20] { Mouse.s } under SafeFast    // Where is Mouse under SafeFast?</formula>
			<comment>Expect the location trajectory to home-in to 2,3,5,6 (just like Fast), but occasionally get distracted to other places of the maze.</comment>
		</query>
		<query>
			<formula>simulate [&lt;=100] { Cat.s, Mouse.s } under SafeFast // Cat and Mouse trajectories under SafeFast</formula>
			<comment/>
		</query>
		<query>
			<formula>simulate [&lt;=100; 104] { 13*(Cat.s==Mouse.s), Cat.s, Mouse.s } : 1 : Cat.s==Mouse.s under SafeFast // Find trajectory of Cat catching Mouse using SafeFast</formula>
			<comment>Expect failure as such trace does ont exist, and the estimated probability is less than 5% with 99% confidence level.</comment>
			<option key="--alpha" value="0.01"/>
		</query>
		<query>
			<formula>Pr[&lt;=1000](&lt;&gt; Cat.s == Mouse.s) under SafeFast     // Probability of Cat catching Mouse using SafeFast</formula>
			<comment>Expect probability less than 1% with 99% confidence level -- virtually impossible.</comment>
			<option key="--alpha" value="0.01"/>
			<option key="--epsilon" value="0.01"/>
		</query>
		<query>
			<formula>Pr[&lt;=100](&lt;&gt; Mouse.Cheese) under SafeFast &gt;= Pr[&lt;=100](&lt;&gt; Mouse.Cheese) under Fast  // Which SafeFast or Fast is better for reaching Cheese?</formula>
			<comment>Expect YES, satisfied.
The comparison plot shows 0.5 everywhere, meaning that it could not distinguish the probabilities, 
i.e. probabilities are approximately equal for entire time duration.</comment>
		</query>
		<query>
			<formula>Pr[&lt;=100](&lt;&gt; Mouse.Cheese) under SafeFast          // Probability of Mouse reaching Cheese using SafeFast</formula>
			<comment>Expect probability close to 100%.
Cumulative Probability Distribution shows that it always takes 5 time units -- as good result as using Fast strategy.</comment>
			<option key="--alpha" value="0.005"/>
			<option key="--epsilon" value="0.005"/>
		</query>
	</queries>
</nta>